# How do you simplify #(3/2)! #?

##### 2 Answers

It is undefined since

#### Explanation:

Factorial is only defined for positive integres and 0, ie for

#### Explanation:

Factorials were traditionally defined only for Whole Numbers

and

This did not take into account non-integral and negative numbers.

To the rescue came the Gamma Function

The Gamma Function is defined as a definite integral,

How is the Gamma Function related to the Factorial Function? Well,

The advantage of representing the Factorial in terms of the Gamma function was that we could make use of several of the neat little properties of the Gamma function to evaluate non-integral factorials. One such property states that,

Another property is,

If you use

The number whose factorial we wish to evaluate does not lie between 0 and 1, so we'll make use of Eqn. 1,

This is how you evaluate non-integral values under a factorial. Keep in mind that the Gamma Function explodes for negative-integral values of z.